Abstract
In this paper, a present status in the development of the new numerical code is reported. The code is considered for simulations of fluid flows. The finite volume approach is adopted for solving standard fluid equations. They are treated in a conservative form to ensure a correct conservation of fluid quantities. Thus, a nonlinear hyperbolic system of conservation laws in numerically solved. The code uses the Eulerian description of the fluid and is designed as a high order central numerical scheme. The central approach employs no (approximate) Riemann solver and is less computational expensive. The high order WENO strategy is adopted in the reconstruction step to achieve results comparable with more accurate Riemann solvers. A combination of the central approach with an iterative solving of a local Riemann problem is tested and behaviour of such numerical flux is reported. An extension to three dimensions is implemented using a dimension by dimension approach, hence, no complicated dimensional splitting need to be introduced. The code is fully parallelized with the MPI library. Several standard hydrodynamic tests in one, two and three dimensions were performed and their results are presented.
Similar content being viewed by others
References
X. D. Liu, E. Tadmor:Third order nonoscillatory central scheme for hyperbolic conservation laws, Numerische Matematik79 (1998) 397.
A. Kurganov, S. Noelle, G. Petrova:Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM Journal on Scientific Computing23 (2001) 707.
V. A. Titarev, E. F. Toro:Finite-volume WENO schemes for three-dimensional conservation laws, J. Computational Physics, submitted.
S. Gottlieb, Chi. W. Shu, E. Tadmor:Strong Stability Preserving High-order Time Discretization Methods. NASA/ICASE Report No. 200–15 (2000).
R. Liska, B. Wendroff:Comparison of several difference schemes on 1D and 2D test problems for the Euler equations, SIAM Journal on Scientific Computing25 (2003) 995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Skandera, D. 3D code for simulations of fluid flows. Czech. J. Phys. 54 (Suppl 3), C59–C64 (2004). https://doi.org/10.1007/BF03166380
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03166380